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Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies

Alexander Lorz, Tommaso Lorenzi, Michael E. Hochberg, Jean Clairambault, Benoît Perthame (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death...

Positive solutions of a renewal equation

Janusz Traple (1992)

Annales Polonici Mathematici

An existence theorem is proved for the scalar convolution type integral equation x ( t ) = ∫ - ∞ ∞ h ( t - s ) f ( s , x ( s ) ) d s .

Remarks on existence of positive solutions of some integral equations

Jan Ligęza (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We study the existence of positive solutions of the integral equation x ( t ) = μ ∫ 0 1 k ( t , s ) f ( s , x ( s ) , x ' ( s ) , ... , x ( n - 1 ) ( s ) ) d s , n ≥ 2 in both C n - 1 [ 0 , 1 ] and W n - 1 , p [ 0 , 1 ] spaces, where p ≥ 1 and μ > 0 . Throughout this paper k is nonnegative but the nonlinearity f may take negative values. The Krasnosielski fixed point theorem on cone is used.

Stability analysis of reducible quadrature methods for Volterra integro-differential equations

Vernon L. Bakke, Zdzisław Jackiewicz (1987)

Aplikace matematiky

Stability analysis for numerical solutions of Voltera integro-differential equations based on linear multistep methods combined with reducible quadrature rules is presented. The results given are based on the test equation y ' ( t ) = γ y ( t ) + ∫ 0 t ( λ + μ t + v s ) y ( s ) d s and absolute stability is deffined in terms of the real parameters γ , λ , μ and v . Sufficient conditions are illustrated for ( 0 ; 0 ) - methods and for combinations of Adams-Moulton and backward differentiation methods.

Stability criteria of linear neutral systems with distributed delays

Guang-Da Hu (2011)

Kybernetika

In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded...

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